I’ll look at the Salice hinge. The only possible solution I can make out using Blum (which I really like) is to block behind the face frame as you mentioned, which mimics a frameless situation, and then use the Blum half-cranked for inset doors, with the frameless mounting plate pulled forward 3/8”. But even there, the lip might bind on opening.
My fallback is a nice Italian hinge where only the pivot shows, but it’s not self-closing.
Thanks for trying!